χ2 Goodness of Fit Test of V2 Bomb Hits

Over the period considered, the total number of fallen bombs within the 576 squares was 537. The actual results were as follow:

The average number of hits per square(μ) is then 537/576=.9323 hits per square. If the targeting is completely random, then the probability that a square is hit with 0,1,2,3 etc hits is governed by a Poisson distribution of which the probability distribution is as follows:

Then, the expected numbers of squares were calculated from the Poisson formula as the third column of the table below:

For instance, 226.7 in the third column can be obtained as follows:

Then, the predicted number(on average) of squares out of 576 in which there are no bomb hits Likewise, other numbers in the column 3 can be easily obtained. The occurrence of clustering would have been reflected in the above table by an excess number of squares containing either a high number of flying bombs or none at all, with a deficiency in the intermediate classes. This is an instructive illustration: to the untrained eye, randomness appears as tendency to cluster. To statistically test the actual fit of the Poisson for the data, a χ2 test to the comparison of actual with expected figures can be conducted as follows:

Since 1.17 is much less than 13.3( , H0 cannot be rejected: the actual fit of the Poisson for the data is surprisingly good, which in fact lends no support to the clustering hypothesis(H1).